“Which Proof for Which Class?”: Factors Influencing the Selection of Mathematical Proofs for Teaching

Selecting a proof for teaching is a frequent task for teachers. However, it is so far unclear, which factors are considered by teachers when selecting proofs. Is the selection based on task and proof characteristics such as the didactical type of proof? Or based on class characteristics such as students’ algebraic skills? Or do teachers’ characteristics such as their proof skills govern their decision? Or is the selection too non-generic for these characteristics to show a meaningful impact? To address these questions, a quasi-experimental study with N= 183 pre-service teachers was conducted to evaluate the influence of each of these factors on their selection of proofs for teaching. Results highlight several significant effects of the abovementioned characteristics and underline that—even at the pre-service level—the selection of proofs is more nuanced than often assumed in prior research and that teachers deliberately and adaptively select proofs for their teaching based on these factors.